Adaptive residual subsampling methods for radial basis function interpolation and collocation problems

Authors:
Tobin A. Driscoll;Alfa R. H. Heryudono
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, United States;Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, United States
Venue:
Computers & Mathematics with Applications
Year:
2007

Citing 6
Cited 17

Moving mesh methods based on moving mesh partial differential equations

Journal of Computational Physics
Solving partial differential equations by collocation using radial basis functions

Applied Mathematics and Computation
Adaptive radial basis function methods for time dependent partial differential equations

Applied Numerical Mathematics
Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation

SIAM Journal on Numerical Analysis
Stable computation of multiquadric interpolants for all values of the shape parameter

Computers & Mathematics with Applications
Computing eigenmodes ofelliptic operators using radial basis functions

Computers & Mathematics with Applications

The Runge phenomenon and spatially variable shape parameters in RBF interpolation

Computers & Mathematics with Applications
Radial function collocation solution of partial differential equations in irregular domains

International Journal of Computing Science and Mathematics
An iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities

Applied Numerical Mathematics
Integrated Radial Basis Function Networks with Adaptive Residual Subsampling Training Method for Approximation and Solving PDEs

ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part II
Rational radial basis function interpolation with applications to antenna design

Journal of Computational and Applied Mathematics
Error saturation in Gaussian radial basis functions on a finite interval

Journal of Computational and Applied Mathematics
Recovery of High Order Accuracy in Radial Basis Function Approximations of Discontinuous Problems

Journal of Scientific Computing
Numerical solution of PDEs via integrated radial basis function networks with adaptive training algorithm

Applied Soft Computing
Iterative adaptive RBF methods for detection of edges in two-dimensional functions

Applied Numerical Mathematics
Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval

Computers & Mathematics with Applications
Numerical experiments on the condition number of the interpolation matrices for radial basis functions

Applied Numerical Mathematics
Adaptive methods for center choosing of radial basis function interpolation: a review

ICICA'10 Proceedings of the First international conference on Information computing and applications
Spectral collocation and radial basis function methods for one-dimensional interface problems

Applied Numerical Mathematics
Optimal constant shape parameter for multiquadric based RBF-FD method

Journal of Computational Physics
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode

SIAM Journal on Scientific Computing
Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers

Journal of Scientific Computing
A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.09

Visualization

Abstract

We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initial-boundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the interpolation matrix. The performance of the method is shown in numerical examples in one and two space dimensions with nontrivial domains.